alanr0
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Senior Member
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Posts: 2,562
Diffraction and Depth of Field
2
Garry2306 wrote:
BTW, purely for self education reasons, and the fact I’m about to try some ultra macro photography, I just posted a few thoughts on my blog, that some may find of interest.
I not claiming anything new here, as I say, my posting is cathartic in nature
https://photography.grayheron.net/2021/08/continung-insights-into-macro.html
Thanks for posting Garry. Some observations based on my own analysis:
In your root-sum-of-squares expression, you appear to equate the diameter of the geometric blur, c, with the diameter of the first dark ring of the Airy disk, 2.44 λ N, where N is the f-number and λ is the wavelength. As you point out, this is approximately equal to 4 N/3 for visible light, and more precisely for 546 nm green light.
Diffraction blur has a much weaker subjective impact than a 'top hat' geometric blur of the same diameter as the first dark ring of the Airy PSF. Arguably, better metrics might be the full width at half maximum (1.08 λ N) or the 1/e² diameter (roughly 1.64 λ N) often used to characterise blur diameter or spot size.
Yet another metric is the diameter of the geometric Circle of Confusion which gives the same MTF50 (modulation transfer function at 50% contrast) as the diffraction blur. This is approximately 1.7 λ N.
Combined diffraction and defocus
A further complication is that the root sum of squares combination of blurs is not particularly accurate, especially for small amounts of defocus. If you examine how the point spread function varies with defocus we do not see a simple monotonic broadening.
Intensity variation with defocus: https://en.wikipedia.org/wiki/File:Spherical-aberration-slice.jpg#file
Consider the central image (above) for image defocus with no spherical aberration.
For small defocus (image plane left or right of best focus), the intensity of the central peak of the Airy disk decreases, but does not get significantly narrower. Instead, an increasing proportion of the total energy is pushed outwards into the diffraction rings. At larger defocus, the geometric optics description of a uniform circular blur becomes more accurate.
In another series of threads back in 2016, I developed an alternative root sum of squares approximation for MTF50 which made some allowance for these effects. Not as coherent and easy to follow as your blog, but if you are interested, here is a summary with links to the original threads.
Getting back to your macro photograph, with moderate amounts of diffraction and defocus, the blur point spread function is not dissimilar to a simple Gaussian, and can respond well to sharpening in post-processing. You may have better results with smaller apertures (higher f-number) than your present analysis predicts. Worth investigating, at any rate. https://rawpedia.rawtherapee.com/Sharpening
Cheers.